Disorientations after Severe Plastic Deformation and their Effect on Work-Hardening

Plastic deformation creates orientation differences in grains of originally uniform orientation. These disorientations are caused by a local excess of dislocations having the same sign of the Burgers vector. Their increase with increasing plastic strain is modeled by dislocation dynamics taking into account different storage mechanisms. The predicted average disorientation angles across different types of boundaries are in close agreement with experimental data for small and moderate plastic strains. At large plastic strains after severe plastic deformation, saturation of the measured average disorientation angle is observed. This saturation is explained as an immediate consequence of the restriction of experimentally measured disorientation angles to angles below a certain maximum value imposed by crystalline symmetry. Taking into account the restrictions from crystalline symmetry for modeled disorientation angles does not only lead to an excellent agreement with experimental findings on Ni after high pressure torsion, but also rationalizes the work-hardening behavior at large plastic strains as well as a saturation of the flow stress.

Maximum disorientation angles between crystals of any point groups and their corresponding rotation axes

The symmetry-reduced misorientation,i.e.disorientation, between two crystals is represented in the angle–axis format, and the maximum disorientation angle between any two lattices of the 32 point groups is obtained by constructing the fundamental zone of the associated misorientation space (i.e.Rodrigues–Frank space) using quaternion algebra. A computer program based on vertex enumeration was designed to automatically calculate the vertices of these fundamental zones and to seek the maximum disorientation angles and respective rotation axes. Of the C_{32}^2 = 528 possible combinations of any two crystals, 129 pairs give rise to incompletely bounded fundamental zones (i.e.zones having at least one unbounded direction inR3); these correspond to a maximum disorientation angle of 180° (the trivial value). The other 399 pairs produce fully bounded fundamental zones that lead to nine different nontrivial maximum disorientation angles; these are 56.60, 61.86, 62.80, 90, 90.98, 93.84, 98.42, 104.48 and 120°. The associated rotation axes were obtained and are plotted in stereographic projection. These angles and axes are solely determined by the symmetries of the point groups under consideration, and the only input data needed are the symmetry operators of the lattices.

Modeling and Simulation of the Percolation Problem in High-Tc Superconductors: Role of Crystallographic Constraints on Grain Boundary Connectivity

Superconductivity in high-Tc materials is often modeled as a percolation problem in which grain boundaries are classified as strong or weak-links for current transmission based on their disorientation angle. Using Monte Carlo simulations, we have explored the topology and percolation thresholds for grain boundary networks in orthorhombic and tetragonal polycrystals where the grain boundary disorientations are assigned in a crystallographically consistent manner. We find that the networks are highly nonrandom, and that the percolation thresholds differ from those found with standard percolation theory. For biaxially textured materials, we have also developed an analytical model that illustrates the role of local crystallographic constraint on the observed nonrandom behavior.